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Statistical Methods with Applications to Demography and Life Insurance
book

Statistical Methods with Applications to Demography and Life Insurance

by Estate V. Khmaladze
March 2013
Intermediate to advanced content levelIntermediate to advanced
242 pages
5h 47m
English
Chapman and Hall/CRC
Content preview from Statistical Methods with Applications to Demography and Life Insurance
Lecture 10
Kaplan–Meier estimator
(product-limit estimator) for F
Now we can introduce the desired estimator for the distribution func-
tion F of lifetimes, based on censored observations.
Since M
n
accumulates the “purely noisy” component of N
n
, we
obtain our estimator by equating M
n
to zero, that is, as a solution to the
equation
N
n
(t)
Z
t
0
Y
n
(y)
dF(y)
1 F(y)
= 0, 0 t
e
T
(n)
, (10.1)
with respect to F. Here
e
T
(n)
is the moment of the last jump of the
process Y
n
.
For piece-wise constant function N
n
(t) with jumps, and all trajec-
tories of N
n
(t) are such functions, the solution is given by
1 F
n
(t) =
y<t
1
dN
n
(y)
Y
n
(y)
, 0 t
e
T
(n)
.
The function F
n
is called the ...
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Publisher Resources

ISBN: 9781466505742